On the distribution of barriers in the spin glasses

We discuss a general formalism that allows study of transitions over barriers in spin glasses with long-range interactions that contain large but finite number, $N$, of spins. We apply this formalism to the Sherrington-Kirkpatrick model with finite $N$ and derive equations for the dynamical order parameters which allow ''instanton'' solutions describing transitions over the barriers separating metastable states. Specifically, we study these equations for a glass state that was obtained in a slow cooling process ending a little below $T_{c}$ and show that these equations allow ''instanton'' solutions which erase the response of the glass to the perturbations applied during the slow cooling process. The corresponding action of these solutions gives the energy of the barriers, we find that it scales as $\tau ^{6}$ where $\tau$ is the reduced temperature.Comment: 8 pages, LaTex, 2 Postscript figure

Multi-frequency scatter broadening evolution of pulsars - I

We present multi-wavelength scatter broadening observations of 47 pulsars, made with the Giant Metre-wave Radio Telescope (GMRT), Ooty Radio Telescope (ORT) and Long Wavelength Array (LWA). The GMRT observations have been made in the phased array mode at 148, 234, and 610 MHz and the ORT observations at 327 MHz. The LWA data sets have been obtained from the LWA pulsar data archive. The broadening of each pulsar as a function of observing frequency provides the frequency scaling index, $\alpha$. The estimations of $\alpha$ have been obtained for 39 pulsars, which include entirely new estimates for 31 pulsars. This study increases the total sample of pulsars available with $\alpha$ estimates by $\sim$50\%. The overall distribution of $\alpha$ with the dispersion measure (DM) of pulsar shows interesting variations, which are consistent with the earlier studies. However, for a given value of DM a range of $\alpha$ values are observed, indicating the characteristic turbulence along each line of sight. For each pulsar, the estimated level of turbulence, $C^{2}_{n_e}$, has also been compared with $\alpha$ and DM. Additionally, we compare the distribution of $\alpha$ with the theoretically predicated model to infer the general characteristics of the ionized interstellar medium (ISM). Nearly 65\% of the pulsars show a flatter index (i.e., $\alpha < 4.4$) than that is expected from the Kolmogorov turbulence model. Moreover, the group of pulsars having flatter index is typically associated with an enhanced value of $C^{2}_{n_e}$ than those with steeper index.Comment: 13 pages, 4 figures, 3 tables. Accepted for publication in Ap